The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  0  1  1  1  1  1  X  X  1  0  1  1  1  1  1  1  1  X  1  1  1
 0  X 2X  0 2X^2+X 2X  0 2X^2+X 2X X^2 2X^2+X 2X X^2+2X  0 2X^2+X X^2+X X^2+2X X^2 2X  0 2X^2+X X^2+X 2X X^2+2X X^2  X 2X 2X^2 2X^2+2X  0  X 2X^2+X 2X^2+X X^2 2X  X X^2+2X 2X X^2+2X 2X  X 2X^2+X 2X 2X^2  X 2X^2+X  X  X X^2+X X^2 X^2+X 2X^2+2X 2X^2+X X^2 2X^2+2X  0
 0  0 X^2  0  0  0  0 2X^2 X^2  0 X^2 2X^2 2X^2  0  0 X^2  0  0 X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2  0 2X^2 X^2 X^2 2X^2 2X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 2X^2 2X^2 2X^2 X^2  0 X^2  0  0
 0  0  0 X^2  0  0  0  0  0 2X^2  0 X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 2X^2  0  0 2X^2 2X^2 2X^2 X^2  0  0 X^2 2X^2 2X^2  0  0  0 X^2 2X^2 2X^2  0 2X^2 X^2 X^2 X^2  0 2X^2 X^2 2X^2 X^2  0  0 2X^2  0  0
 0  0  0  0 2X^2  0 X^2 2X^2 X^2 X^2  0 X^2 2X^2  0 2X^2  0 2X^2  0 2X^2 2X^2  0  0  0 X^2 X^2  0  0 2X^2 2X^2 2X^2 2X^2  0 2X^2 X^2 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2 X^2  0 X^2 X^2 2X^2 X^2  0 2X^2  0  0 2X^2  0 2X^2 X^2 2X^2
 0  0  0  0  0 X^2 X^2  0 2X^2 X^2  0  0 X^2 X^2 2X^2 2X^2 X^2 X^2  0 2X^2  0  0 2X^2 X^2 X^2 X^2 X^2 X^2  0  0 2X^2 X^2 X^2 X^2  0 2X^2 X^2 X^2  0 X^2 2X^2 2X^2 2X^2  0  0  0  0  0 2X^2 X^2 2X^2 X^2  0 2X^2  0  0

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 99.

Homogenous weight enumerator: w(x)=1x^0+58x^99+30x^100+6x^101+350x^102+108x^103+66x^104+440x^105+378x^106+192x^107+1520x^108+1188x^109+342x^110+4406x^111+2202x^112+474x^113+4430x^114+1608x^115+294x^116+636x^117+186x^118+84x^119+324x^120+120x^121+120x^123+12x^124+46x^126+24x^129+10x^132+14x^135+6x^138+4x^141+2x^144+2x^147

The gray image is a linear code over GF(3) with n=504, k=9 and d=297.
This code was found by Heurico 1.16 in 1.93 seconds.